Instrumental variable additive hazards models.

Instrumental variables (IVs) methods have recently gained popularity since, under certain assumptions, they may yield consistent causal effect estimators in the presence of unmeasured confounding. Existing simulation studies that evaluate the performance of IV approaches for time-to-event outcomes tend to consider either an additive or a multiplicative data-generating mechanism (DGM) and have been limited to an exponential constant baseline hazard model. In particular, the relative merits of additive versus multiplicative IV models have not been fully explored. All IV methods produce less biased estimators than naïve estimators that ignore unmeasured confounding, unless the IV is very weak and there is very little unmeasured confounding. However, the mean squared error of IV estimators may be higher than that of the naïve, biased but more stable estimators, especially when the IV is weak, the sample size is small to moderate, and the unmeasured confounding is strong. In addition, the sensitivity of IV methods to departures from their assumed DGMs differ substantially. Additive IV methods yield clearly biased effect estimators under a multiplicative DGM whereas multiplicative approaches appear less sensitive. All can be extremely variable. We would recommend that survival probabilities should always be reported alongside the relevant hazard contrasts as these can be more reliable and circumvent some of the known issues with causal interpretation of hazard contrasts. In summary, both additive IV and Cox IV methods can perform well in some circumstances but an awareness of their limitations is required in analyses of real data where the true underlying DGM is unknown.

BackgroundTwo-stage least square [2SLS] and two-stage residual inclusion [2SRI] are popularly used instrumental variable (IV) methods to address medication nonadherence in pragmatic trials with point treatment settings. These methods require assumptions, e.g., exclusion restriction, although they are known to handle unmeasured confounding. The newer IV-method, nonparametric causal bound [NPCB], showed promise in reducing uncertainty compared to usual IV-methods. The inverse probability-weighted per-protocol [IP-weighted PP] method is useful in the same setting but requires different assumptions, e.g., no unmeasured confounding. Although all of these methods are aimed to address the same nonadherence problem, comprehensive simulations to compare performances of them are absent in the literature.MethodsWe performed extensive simulations to compare the performances of the above methods in addressing nonadherence when: (1) exclusion restriction satisfied and no unmeasured confounding, (2) exclusion restriction is met but unmeasured confounding present, and (3) exclusion restriction is violated. Our simulations varied parameters such as, levels of adherence rates, unmeasured confounding, and exclusion restriction violations. Risk differences were estimated, and we compared performances in terms of bias, standard error (SE), mean squared error (MSE), and 95% confidence interval coverage probability.ResultsFor setting (1), 2SLS and 2SRI have small bias and nominal coverage. IP-weighted PP outperforms these IV-methods in terms of smaller MSE but produces high MSE when nonadherence is very high. For setting (2), IP-weighted-PP generally performs poorly compared to 2SLS and 2SRI in term of bias, and both-stages adjusted IV-methods improve precision than naive IV-methods. For setting (3), IV-methods perform worst in all scenarios, and IP-weighted-PP produces unbiased estimates and small MSE when confounders are adjusted. NPCB produces larger uncertainty bound width in almost all scenarios. We also analyze a two-arm trial to estimate vitamin-A supplementation effect on childhood mortality after addressing nonadherence.ConclusionsUnderstanding finite sample characteristics of these methods will guide future researchers in determining suitable analysis strategies. Since assumptions are different and often untestable for IP-weighted PP and IV methods, we suggest analyzing data using both IP-weighted PP and IV approaches in search of a robust conclusion.

To contrast the interpretations of treatment effect estimates using risk adjustment and instrumental variable (IV) estimation methods using observational data when the effects of treatment are heterogeneous across patients. We demonstrate these contrasts by examining the effect of breast conserving surgery plus irradiation (BCSI) relative to mastectomy on early stage breast cancer (ESBC) survival. We estimated discrete time survival models for 6185 ESBC patients in the 1989-1994 Iowa Cancer Registry via IV estimation using 2 distinct instruments (distance of the patient's residence from the nearest radiation center, and local area BCSI rate) and controlling for cancer stage, grade, and location; age; comorbidity; hospital access; payer; diagnosis year; and area poverty level. We then estimated comparable risk adjustment survival models using linear probability methods with robust standard errors. Risk adjustment models yielded average survival estimates similar to trial results. With favorable BCSI selection, these estimates represent an upper bound of the true effect for patients receiving BCSI. IV estimates showed a BCSI survival risk for patients whose surgery choices were affected by the instruments and these estimates varied with the instrument specification. When treatment benefits are heterogeneous across patients, treatment effect estimates from observational data can still be useful to policymakers, but they must be interpreted correctly. Risk adjustment methods yield estimates that can assess whether the patients who received treatment benefited from the treatment, but the direction of bias must be considered. In contrast, IV estimates can assess the effect of treatment rate changes, but characteristics of patients whose choices were affected by the instruments must be considered when making such inferences.

In randomised controlled trials that have non-compliance with the treatment assigned, policy makers require unbiased estimates of the causal effect of the treatment received.Instrumental variable (IV) approaches provide complier average causal effects (CACE) estimates.Common IV methods such as two-stage least squares (2SLS) have not been extended to settings with multivariate outcomes.We propose a three-stage least squares (3SLS) regression approach, whereby estimates from the first stage regression of treatment received conditional on assignment, feed into a seemingly unrelated regression (SUR) system of equations that recognise the correlation between the outcomes.We also develop Bayesian IV approaches which jointly model the effects of random assignment on treatment received, and the bivariate outcome, which here is assume to be cost-effectiveness.We also apply 2SLS individually to each outcome, for comparison.We consider the performance of these methods in a simulation study, where costs are assumed to follow Normal or Gamma distributions, to have positive and negative correlation with health outcomes, the instrument is strong (30% non-compliance) or weak (70% noncompliance), and the sample size, moderate (n=1,000) or small (n=100).We find that the proposed IV methods generally perform well.For example, in scenarios with Normally distributed cost data and a strong instrument, each method reports unbiased estimates.However, in these settings the 2SLS approach reports levels of Confidence Interval (CI) coverage that are above (positive correlation) and below (negative correlation) nominal levels.By contrast both the 3SLS and Bayesian methods report CI coverage close to nominal levels.

Instrumental variable (IV) methods have been proposed as a potential approach to the common problem of uncontrolled confounding in comparative studies of medical interventions, but IV methods are unfamiliar to many researchers. The goal of this article is to provide a non-technical, practical introduction to IV methods for comparative safety and effectiveness research. We outline the principles and basic assumptions necessary for valid IV estimation, discuss how to interpret the results of an IV study, provide a review of instruments that have been used in comparative effectiveness research, and suggest some minimal reporting standards for an IV analysis. Finally, we offer our perspective of the role of IV estimation vis-à-vis more traditional approaches based on statistical modeling of the exposure or outcome. We anticipate that IV methods will be often underpowered for drug safety studies of very rare outcomes, but may be potentially useful in studies of intended effects where uncontrolled confounding may be substantial.

We studied the application of the generalized structural mean model (GSMM) of instrumental variable (IV) methods in estimating treatment odds ratios (ORs) for binary outcomes in pharmacoepidemiologic studies and evaluated the bias of GSMM compared to other IV methods. Because of the bias of standard IV methods, including two-stage predictor substitution (2SPS) and two-stage residual inclusion (2SRI) with binary outcomes, we implemented another IV approach based on the GSMM of Vansteelandt and Goetghebeur. We performed simulations under the principal stratification setting and evaluated whether GSMM provides approximately unbiased estimates of the causal OR and compared its bias and mean squared error to that of 2SPS and 2SRI. We then applied different IV methods to a study comparing bezafibrate versus other fibrates on the risk of diabetes. Our simulations showed that unlike the standard logistic, 2SPS, and 2SRI procedures, our implementation of GSMM provides an approximately unbiased estimate of the causal OR even under unmeasured confounding. However, for the effect of bezafibrate versus other fibrates on the risk of diabetes, the GSMM and two-stage approaches yielded similarly attenuated and statistically non-significant OR estimates. The attenuation of the OR by the two-stage and GSMM IV approaches suggests unmeasured confounding, although violations of the IV assumptions or differences in the parameters estimated could be playing a role. The GSMM IV approach provides approximately unbiased adjustment for unmeasured confounding on binary outcomes when a valid IV is available.

Background:Survival rates for breast cancer (BC) are often based on the outcomes of this disease. The aim of this study was to compare the performance of three survival models, namely Cox regression, Aalen's, and Lin and Ying's additive hazards (AH) models for identifying the prognostic factors regarding the survival time of BC patients.Materials and Methods:This study was a historical cohort study which used 1025 females' medical records that underwent modified radical mastectomy or breast saving. These patients were admitted to Besat and Chamran Hospitals, Tehran, Iran, during 2010–2015 and followed until 2017. The Aalen's and Lin and Ying's AH models and also traditional Cox model were applied for analysis of time to death of BC patients using R 3.5.1 software.Results:In Aalen's and also Lin and Ying's AH models, age at diagnosis, history of disease, number of lymph nodes, metastasis, hormonal therapy, and evacuation lymph nodes were prognostic factors for the survival of BC patients (P < 0.05). In addition, in the Lin and Ying's AH model tumor size (P = 0.048) was also identified as a significant factor. According to Aalen's plot, metastasis, age at diagnosis, and number of lymph nodes had a time-varying effect on survival time. These variables had a different slope as the times go on.Conclusion:AH model may yield new insights in prognostic studies of survival time of patients with BC over time. Because of the positive slope of estimated cumulative regression function in Aalen's plot, metastasis, higher age at diagnosis, and high number of lymph nodes are important factors in reducing the survival BC, and then based on these factors, the therapists should consider a special therapeutic protocol for BC patients.

On the Use of Instrumental Variables in Accounting Research

Medical cost data often consist of zero values as well as extremely right-skewed positive values. A two-part model is a popular choice for analyzing medical cost data, where the first part models the probability of a positive cost using logistic regression and the second part models the positive cost using a lognormal or Gamma distribution. To address the unmeasured confounding in studies on cost outcome under two-part models, two instrumental variable (IV) methods, two-stage residual inclusion (2SRI) and two-stage prediction substitution (2SPS) are widely applied. However, previous literature demonstrated that both the 2SRI and the 2SPS could fail to consistently estimate the causal effect among compliers under standard IV assumptions for binary and survival outcomes. Our simulation studies confirmed that it continued to be the case for a two-part model, which is another nonlinear model. In this article, we develop a model-based IV approach, Instrumental Variable with Two-Part model (IV2P), to obtain a consistent estimate of the causal effect among compliers for cost outcome under standard IV assumptions. In addition, we develop sensitivity analysis approaches to allow the evaluation of the sensitivity of the causal conclusions to potential quantified violations of the exclusion restriction assumption and the randomization of IV assumption. We apply our method to a randomized cash incentive study to evaluate the effect of a primary care visit on medical cost among low-income adults newly covered by a primary care program.

Goodness-of-fit tests for Cox's proportional hazards model and Aalen's additive risk model, in which each model is compared on an equal footing with the best fitting fully nonparametric model, are developed. The goodness-of-fit statistics are based on differences each model, with a fully nonparametric estimator of d recently introduced by the authors. Here A( , z) denotes the conditional hazard function of the survival time of an individual with covariate vector z. Comparison of the results of the tests makes it possible to decide whether Cox's proportional hazards or Aalen's additive risk model gives a better fit to the data. In addition, a goodness-of-fit test for Cox's model within the family of all proportional hazards models A(t, z) = AO(t)r(z), where AO is a baseline hazard function and r is a general relative risk function, is developed. Additive hazards and proportional hazards regression models used in the analysis of censored survival data can give substantially different results. For instance, in connection with a study of cancer mortality among Japanese atomic bomb survivors, Muirhead & Darby (1987) have noted that the two models give substantially different estimates of the age-spe- cific probability that an individual will develop radiation induced cancer. Muirhead & Darby (see also Aranda-Ordaz, 1983) introduced a generalized parametric model which contains parametric additive hazards and proportional hazards models as special cases. The goodness- of-fit of each model is then obtained by comparing with the best fitting model within the generalized family, allowing the two special models to be treated on an equal footing. Beyond the parametric setting, much effort has been devoted to the development of goodness-of-fit tests for Cox's (1972) proportional hazards model

Additive time-dependent hazard model with doubly truncated data

We hypothesize that analyzing individual-level secondary data with instrumental variable (IV) methods can advance knowledge of the long-term effects of air pollution on dementia. We discuss issues in measurement using secondary data and how IV estimation can overcome biases due to measurement error and unmeasured variables. We link air-quality data from the Environmental Protection Agency’s monitors with Medicare claims data to illustrate the use of secondary data to document associations. Additionally, we describe results from a previous study that uses an IV for pollution and finds that PM2.5’s effects on dementia are larger than non-causal associations.

The instrumental variable (IV) approach is a widely used way to estimate the causal effects of a treatment on an outcome of interest from observational data with latent confounders. A standard IV is expected to be related to the treatment variable and independent of all other variables in the system. However, it is challenging to search for a standard IV from data directly due to the strict conditions. The conditional IV (CIV) method has been proposed to allow a variable to be an instrument conditioning on a set of variables, allowing a wider choice of possible IVs and enabling broader practical applications of the IV approach. Nevertheless, there is not a data-driven method to discover a CIV and its conditioning set directly from data. To fill this gap, in this paper, we propose to learn the representations of the information of a CIV and its conditioning set from data with latent confounders for average causal effect estimation. By taking advantage of deep generative models, we develop a novel data-driven approach for simultaneously learning the representation of a CIV from measured variables and generating the representation of its conditioning set given measured variables. Extensive experiments on synthetic and real-world datasets show that our method outperforms the existing IV methods.

In the disciplines of medicine, biology and social science, causal mediation analysis is widely used to examine the effect of an exposure on an outcome through different causal pathways. Recently, there is rapid development of mediation analysis with survival data. An early work of Lange and Hansen proposed to identify the direct and indirect causal effects under the additive hazards model with a single mediator. However, inaccurate measurements of mediators and confounders may lead to biased causal effect estimation. We propose a measurement error correction approach to tackle measurement error in the mediators and confounders under the additive hazards model where multiple mediators are present. We apply the proposed corrected method to the ACTG175 Study data set, and uncover interesting findings.

Background:One substantial part of microarray studies is to predict patients’ survival based on their gene expression profile. Variable selection techniques are powerful tools to handle high dimensionality in analysis of microarray data. However, these techniques have not been investigated in competing risks setting. This study aimed to investigate the performance of four sparse variable selection methods in estimating the survival time.Methods:The data included 1381 gene expression measurements and clinical information from 301 patients with bladder cancer operated in the years 1987 to 2000 in hospitals in Denmark, Sweden, Spain, France, and England. Four methods of the least absolute shrinkage and selection operator, smoothly clipped absolute deviation, the smooth integration of counting and absolute deviation and elastic net were utilized for simultaneous variable selection and estimation under an additive hazards model. The criteria of area under ROC curve, Brier score and c-index were used to compare the methods.Results:The median follow-up time for all patients was 47 months. The elastic net approach was indicated to outperform other methods. The elastic net had the lowest integrated Brier score (0.137±0.07) and the greatest median of the over-time AUC and C-index (0.803±0.06 and 0.779±0.13, respectively). Five out of 19 selected genes by the elastic net were significant (P<0.05) under an additive hazards model. It was indicated that the expression of RTN4, SON, IGF1R and CDC20 decrease the survival time, while the expression of SMARCAD1 increase it.Conclusion:The elastic net had higher capability than the other methods for the prediction of survival time in patients with bladder cancer in the presence of competing risks base on additive hazards model.